Relation between Change in Potential Energy and Work Done

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Homework Help Overview

The discussion revolves around the relationship between change in potential energy and work done, specifically in the context of conservative forces. Participants are exploring the mathematical expression relating these concepts.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the reasoning behind the equation dU = -\vec{F} \cdot d\vec{r} and its integration leading to ΔU = -W. There are inquiries about whether this relationship is proven or simply defined.

Discussion Status

The conversation includes clarifications about the definition of potential energy and its relation to work done by conservative forces. Some participants assert that it is a definition rather than a theorem requiring proof, while others seek further understanding of this assertion.

Contextual Notes

There is a focus on conservative forces, with participants noting that the relationship discussed applies specifically to these types of forces.

andyrk
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Why is dU=-[itex]\vec{F}[/itex].d[itex]\vec{r}[/itex]
Integrating with putting the limits on we get:
ΔU=-W
Why is this? Here [itex]\vec{F}[/itex] is a conservative force/Force field.
 
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Potential Energy is actually defined that way. It doesn't require a proof.
 
yup! :smile:

definition! :wink:

(also applies eg to gravity)

(and only works for conservative forces)
 

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